Abbreviated Journal Title
Phys. Rev. A
BOND POTTS MODELS; ISING-MODEL; QUANTUM COMPUTATION; CRITICAL-BEHAVIOR; TRANSFER-MATRIX; TRANSITION; COMPUTER; MEMORY; Optics; Physics, Atomic, Molecular & Chemical
The surface code is a promising alternative for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attractive features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. For the case of a bit-flipping environment, we map the complete evolution after one quantum error correction cycle onto the problem of computing correlation functions of a two-dimensional Ising model with boundary fields. Exact results for the fidelity threshold of the surface code are then obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations.
Physical Review A
Jouzdani, Pejman; Novais, E.; Tupitsyn, I. S.; and Mucciolo, Eduardo R., "Fidelity threshold of the surface code beyond single-qubit error models" (2014). Faculty Bibliography 2010s. 5534.